Δk-radar equivalent of interferometric SAR´s: a theoretical study for determination of vegetation height

Theoretical aspects of estimating vegetation parameters from SAR interferometry are presented. In conventional applications of interferometric SAR (INSAR), the phase of the interferogram is used to retrieve the location of the scattering phase center of the target. Although the location of scattering phase center for point targets can be determined very accurately, for a distributed target such as a forest canopy this is not the case. For distributed targets the phase of the interferogram is a random variable which in general is a function of the system and target attributes. To relate the statistics of the interferogram phase to the target attributes, first an equivalence relationship between the two-antenna interferometer system and an equivalent Δk radar system is established. This equivalence relationship provides a general tool to related the frequency correlation function (FCF) of distributed targets, which can conveniently be obtained experimentally, analytically, or numerically, to the phase statistics of the interferogram. An analytical form for the p.d.f. of the interferogram phase is obtained in terms of two independent parameters: 1) ζ: mean phase and 2) α: degree of correlation. ζ is proportional to the scattering phase center and n is inversely proportional to the uncertainty with which ζ can be estimated. It is shown that α is directly related to the FCF of the distributed target which in turn is a function of scattering mechanisms and system parameters. It is also shown that for a uniform closed canopy the extinction and the physical height of the canopy top can be estimated very accurately. Some analytical and numerical simulations are demonstrated